Ke Zhipeng, Dawson Daniel M, Ashbrook Sharon E, Bühl Michael
School of Chemistry, EaStCHEM and Centre of Magnetic Resonance, University of St Andrews St Andrews KY16 9ST UK
Chem Sci. 2022 Feb 3;13(9):2674-2685. doi: 10.1039/d1sc07138f. eCollection 2022 Mar 2.
An efficient protocol for the calculation of C pNMR shifts in metal-organic frameworks based on Cu(ii) paddlewheel dimers is proposed, which involves simplified structural models, optimised using GFN2-xTB for the high-spin state, and CAM-B3LYP-computed NMR and EPR parameters. Models for hydrated and activated HKUST-1 and hydrated STAM MOFs with one, two and three Cu dimers have been used. The electronic ground states are low-spin and diamagnetic, with pNMR shifts arising from thermal population of intermediate- and high-spin excited states. Treating individual spin configurations in a broken symmetry (BS) approach, and selecting two or more of these to describe individual excited states, the magnetic shieldings of these paramagnetic states are evaluated using the approach by Hrobárik and Kaupp. The total shielding is then evaluated from a Boltzmann distribution between the energy levels of the chosen configurations. The computed pNMR shifts are very sensitive to temperature and, therefore, to the relative energies of the BS spin states. In order to reproduce the temperature dependence of the pNMR shifts seen in experiment, some scaling of the calculated energy gaps is required. A single scaling factor was applied to all levels in any one system, by fitting to experimental results at several temperatures simultaneously. The resulting scaling factor decreases with an increasing number of dimer units in the model (, from ∼1.7 for mono-dimer models to 1.2 for tri-dimer models). The approach of this scaling factor towards unity indicates that models with three dimers are approaching a size where they can be considered as reasonable models for the C shifts of infinite MOFs. The observed unusual temperature dependencies in the latter are indicated to arise both from the "normal" temperature dependence of the pNMR shifts of the paramagnetic states and the populations of these states in the thermal equilibrium.
提出了一种基于Cu(ii)桨轮二聚体计算金属有机框架中C pNMR位移的有效方案，该方案涉及简化的结构模型，使用GFN2-xTB对高自旋态进行优化，并通过CAM-B3LYP计算NMR和EPR参数。已使用具有一个、两个和三个Cu二聚体单元的水合和活化HKUST-1以及水合STAM金属有机框架的模型。电子基态为低自旋且抗磁性，pNMR位移源于中自旋和高自旋激发态的热布居。采用破缺对称性(BS)方法处理单个自旋构型，并选择其中两个或更多来描述单个激发态，使用Hrobárik和Kaupp的方法评估这些顺磁态的磁屏蔽。然后根据所选构型能级之间的玻尔兹曼分布评估总屏蔽。计算得到的pNMR位移对温度非常敏感，因此对BS自旋态的相对能量也很敏感。为了重现实验中观察到的pNMR位移随温度变化的关系，需要对计算得到的能隙进行一些缩放。通过同时拟合几个温度下的实验结果，对任何一个系统中的所有能级应用单个缩放因子。得到的缩放因子随着模型中二聚体单元数量的增加而减小(，从单二聚体模型的约1.7降至三亚聚体模型的1.2)。该缩放因子趋近于1的趋势表明，具有三个二聚体单元的模型正接近一个可以被视为无限金属有机框架C位移合理模型的尺寸。结果表明，后者中观察到的异常温度依赖性既源于顺磁态pNMR位移的“正常”温度依赖性，也源于这些态在热平衡中的布居情况。
